“I think that that would be a fitting tribute,” Flake said on CBS’s “Face the Nation.” “There are many other things that we need to do but that's a good one."

"John McCain had his office just right near mine in the Russell building that's where he was his entire time," he added. "I think that that's a fitting tribute.”

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Schumer announced Saturday shortly after news of McCain's death that he plans to introduce a resolution to rename the building after his longtime colleague in the Senate.

The building is currently named after former Georgia Democratic Sen. Richard Brevard Russell, who opposed numerous efforts to pass civil rights legislation, including bills banning lynching.

Flake served in the House as an Arizona representative for more than a decade, beginning in 2001.

He later moved to the Senate, where he and McCain served as Arizona’s two senators since 2013. Flake announced last year that he would retire in January after one term in the Senate.

Flake also wrote in an op-ed Sunday published in The Washington Post that McCain taught him “the value of standing alone to do what is right.”

McCain died Saturday at age 81 following a battle with an aggressive form of brain cancer. His family announced Friday that they would discontinue treatment for the cancer, saying the “progress of disease and the inexorable advance of age” had rendered “their verdict.”

McCain survived years as a prisoner of war in Vietnam before rising to become a giant of the Senate and a "maverick" of his party.